Prediction of the structure of branched polymers is a challenging problem, for which only more or less
clumsy mathematical solutions have been made available for a long time in the case of kinetically controlled
polymerizations. The matter has, nevertheless, considerable economic significance. For instance,
a controlled amount of long branching is known to have many benefits on the rheologic properties
the widely used polyolefins (Nele et al., 2003). Development of processes and their optimization could
benefit a lot with models with better predictive capacities.
Progresses in applied mathematics could at last bring about a considerable improvement in this situation.
This paper reviews recent methods (Costa and Dias, 2003; Dias and Costa, 2003, 2005) allowing the
direct computation of moments (i. e. avoiding Hulburt-Katz closures) of polymer chain length distributions,
even in the presence of gel, overcoming past difficulties in their computational implementation.
Description of non-linear free radical polymerizations is now possible, thanks to the development
methods for solving highly stiff two point boundary value problems (Cash et. al., 2001). Chain length
distributions are obtained by adapting algorithms better known with Laplace transform inversion (Papoulis,
1956; Weeks, 1966; Durbin, 1974). Numerous past inconsistencies leading to unwanted errors
are now avoided through the use of well-founded chemical and mathematical principles.